Auxiliary Parameter Research Articles

Damage characteristics of coal under different loading modes based on CT three-dimensional reconstruction

Due to the heterogeneous characteristics of coal materials, it is difficult to carry out repetitive tests and quantitative analysis of internal damage of coal. Therefore, the damage characteristics of coal under uniaxial and true triaxial loading was studied by numerical simulation based on 3D reconstruction modeling, and the corresponding mechanics experiment was used for auxiliary parameter validation. Firstly, the CT scanning system was used to scan the coal specimen, and the Otsu method was used to segment the original CT images to extract the three-dimensional fracture network and the distribution characteristics of mineral components. Secondly, the internal fracture and mineral distribution network model of the coal was reconstructed and imported into FLAC3D for modeling, and the numerical model was validated by fractal geometry method. The average error of fractal dimension between the original CT image and the corresponding numerical model is 1.422%, showing that the numerical model is basically consistent with the CT image of the coal, and the numerical model could reflect the distribution characteristics of the internal fractures and mineral components of the coal. Then, the basic mechanical parameters and acoustic emission (AE) response characteristics of CT reconstructed coal samples were obtained. And the mechanical parameters of the numerical model were calibrated. It can be concluded that the stress–strain curve of the coal is basically consistent with that of the numerical model, and the AE response characteristics of the coal are basically consistent with the evolution of the plastic zone of the numerical simulation, indicating that the numerical model and parameters are reasonable in this work. Moreover, the damage variable evolution of coal specimen in uniaxial compression and true triaxial loading was studied. Finally, the damage equation of coal under uniaxial compression and the relationship between damage variable and body strain energy under true triaxial loading were established.

PULSE METHOD FOR DETERMINATION OF TIME PARAMETERS THERMAL FIRE DETECTOR

For thermal fire detectors with a thermoresistive sensitive element, the method of determining its time parameters is justified. The time parameters of operation and the time constant of the thermal fire detector are considered as time parameters. The method is based on the use of the Joule-Lenz effect, for the implementation of which single pulses of electric current are passed through the thermoresistive sensitive element of the fire detector. Pulses having the shape of a quarter sinusoid or a quarter cosinusoid are used as such test signals. Using the Laplace integral transformation, analytical expressions are obtained, which represent the formalization of the reaction of the thermoresistive sensitive element of the fire detector to the corresponding test signals. These analytical expressions are used to obtain the functional dependences of the fire detector time constants on the pulse duration of the electric current and the auxiliary parameter. The auxiliary parameter is the ratio of the values ​​of the output signal of the thermal fire detector at two fixed points in time. This choice of auxiliary parameter allows to ensure invariance with respect to the transfer coefficient of the thermal fire detector with a thermoresistive sensing element. The fixed moments of time are chosen to be equal to half and three quarters of the duration of the pulses of electric current flowing through the thermoresistive sensitive element of the fire detector. The time of operation of the thermal fire detector is determined in the form of two additive components, one of which is a time constant of the fire detector, and the other is determined by the values ​​of normalized parameters in accordance with existing regulations. A sequence of procedures is given, which together represent a method of determining the time parameters of thermal fire detectors of this type.

Diagnostic value of adenosine deaminase in bronchoalveolar lavage fluid for patients with lung cancer.

Lung cancer is both the most common seen malignity and cause of cancer-related deaths worldwide. Adenosine deaminase (ADA) is a hydrolytic enzyme that catalyses the conversion of adenosine to inosine in the purine metabolism pathway. Studies examining ADA levels in bronchoalveolar lavage (BAL) fluids of patients with lung malignancy are very limited in the literature. Our aim examine the clinical significance of ADA levels in BAL fluids of patients with lung malignancy. A total of 89 patients undergoing fiberoptic bronchoscopy (FOB) with different indications from December 2017 to December 2018 were included in this study. The patients were divided into two groups as malignancy and non-malignancy groups. Demographic, laboratory data and ADA levels in bronchoalveolar lavage (BAL) were compared between the two groups. In addition, ADA levels in BAL were compared among the histopathological subtypes of patients in the malignant group. The mean age of the patients was 58.2±14.5years with 86% of male gender. ADA enzyme levels were statistically higher in the malignant patient group compared with the non-malignant group (37.2 [17.6-71] vs 17.1 [9-35.3], P<.001). When the patients in the malignant group were compared in terms of ADA levels according to their histopathological types, a statistically significant difference was obtained in small cell carcinoma patients (49 [12.5-75.3], P=.005). ADA levels in BAL may be a diagnostic biomarker in lung malignancies. In patients where a biopsy cannot be taken or histopathological typing cannot be performed because of tissue insufficiency, ADA levels in BAL can be an auxiliary parameter in making malignancy / histopathological diagnosis accompanied by radiological and clinical findings.

Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials

The new rational a-polynomials are used to solve the Falkner-Skan equation. These polynomials are equipped with an auxiliary parameter. The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients. To find the unknown coefficients and the auxiliary parameter contained in the polynomials, the collocation method with Chebyshev-Gauss points is used. The numerical examples show the efficiency of this method.

The Optimal Homotopy Asymptotic Method for Solving Two Strongly Fractional-Order Nonlinear Benchmark Oscillatory Problems

This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an Optimal Homotopy Asymptotic Method (OHAM), to offer approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems, namely: the fractional-order Duffing-relativistic oscillator and the fractional-order stretched elastic wire oscillator (with a mass attached to its midpoint). In this work, a further modification has been proposed for such method and then carried out through establishing an optimal auxiliary linear operator, an auxiliary function, and an auxiliary control parameter. In view of the two aforesaid applications, it has been demonstrated that the OHAM is a reliable approach for controlling the convergence of approximate solutions and, hence, it is an effective tool for dealing with such problems. This assertion is completely confirmed by performing several graphical comparisons between the OHAM and the Homotopy Analysis Method (HAM).

THE ASYMPTOTICS OF A SOLUTION OF THE MULTIDIMENSIONAL HEAT EQUATION WITH UNBOUNDED INITIAL DATA

For the multidimensional heat equation, the long-time asymptotic approximation of the solution of the Cauchy problem is obtained in the case when the initial function grows at infinity and contains logarithms in its asymptotics. In addition to natural applications to processes of heat conduction and diffusion, the investigation of the asymptotic behavior of the solution of the problem under consideration is of interest for the asymptotic analysisof equations of parabolic type. The auxiliary parameter method plays a decisive role in the investigation.

An efficient hybrid computational technique for the time dependent Lane-Emden equation of arbitrary order

The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life. There are many examples of ocean water waves which are nonlinear in nature. In shallow water, the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water, and the strong nonlinear effects are observed. In this paper, q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order. It offers the solution in a fast converging series. The uniqueness and convergence analysis of the considered model is presented. The given examples confirm the competency as well as accuracy of the presented scheme. The behavior of obtained solution for distinct orders of fractional derivative is discussed through graphs. The auxiliary parameter ħ offers a suitable mode of handling the region of convergence. The outcomes reveal that the q-HATM is attractive, reliable, efficient and very effective.

Empirical Bayesian analysis through the lens of a particular class of constrained Bayesian hierarchical models

Empirical Bayesian analysis is a well-known approach that incorporates an estimator into a Bayesian analysis. In this article, we offer another approach, which has several useful properties. Our solution is based on the framework introduced by Yekutieli (2012) to account for the variability introduced by selecting parameters. Specifically, we assume that the unknown parameter is contained within a ball centered at an estimator, and the radius is given a prior distribution. We refer to our method as the auxiliary parameter constrained Bayesian hierarchical model (C-BHM). This general framework is particularly exciting as traditional empirical Bayesian analysis and parametric Bayesian analysis can be written as special cases. Hence, this C-BHM represents a unifying framework within the area of Bayesian statistics. Several technical results are provided. Furthermore, we show analytically that one can outperform both empirical and fully Bayesian analysis through the Bayes factor. We illustrate the C-BHM to extend the Fay-Herriot model, which is often used in the survey sampling setting. To demonstrate the usefulness of our method we provide simulations and an illustration to data obtained from the U.S. Census Bureau's Small Area Income and Poverty Estimates (SAIPE) program.

Integrable E-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects

We construct the actions of a very broad family of 2d integrable $\sigma$-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This 2d action depends on a pair of 2d fields $h$ and $\mathcal{L}$, with $\mathcal{L}$ depending rationally on an auxiliary complex parameter, which are tied together by a constraint. When the latter can be solved for $\mathcal{L}$ in terms of $h$ this produces a 2d integrable field theory for the 2d field $h$ whose Lax connection is given by $\mathcal{L}(h)$. We construct a general class of solutions to this constraint and show that the resulting 2d integrable field theories can all naturally be described as $\mathcal{E}$-models.

A new computational technique for the analytic treatment of time-fractional Emden–Fowler equations

This paper presents the study of fractional Emden–Fowler (FEF) equations by utilizinga new adequate procedure, specifically the q-homotopy analysis transform method (q-HATM). The EF equation has got greater significance in both physical and mathematical investigation of capillary and nonlinear dispersive gravity waves. The projected technique is tested by considering four illustrations of the time-fractional EF equations. The q-HATM furnish ℏ, known as an auxiliary parameter, by the support of ℏ we can modulate the various stages of convergence of the series solution. Additionally, to certify the resolution and accurateness of the proposed method we fitted the suitable numerical simulations. The redeem results guarantee that the proposed process is more convincing and scrutinizes the extremely nonlinear issues emerging in the field of science and engineering.

On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method

This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through different illustrative numerical examples. The method is shown to be conceptually and computationally simple and straightforward without any ambiguity. Also, the method as applied in this study shows that it does not require the development of any other iterative scheme that could be used to find the solution to the nonlinear equations. Additionally, the method does not require finding symbolic or numerical derivatives of any given function. With the use of the Adomian decomposition method, there is no search for an auxiliary parameter for adjusting and controlling the rate and region of convergence of the solution. The method does not require finding the correct fixed point and it is free from the problem of choosing an appropriate initial approximation. Therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science and engineering.

A Multimethod Analysis for Average Annual Precipitation Mapping in the Khorasan Razavi Province (Northeastern Iran)

The spatial distribution of precipitation is one of the most important climatic variables used in geographic and environmental studies. However, when there is a lack of full coverage of meteorological stations, precipitation estimations are necessary to interpolate precipitation for larger areas. The purpose of this research was to find the best interpolation method for precipitation mapping in the partly densely populated Khorasan Razavi province of northeastern Iran. To achieve this, we compared five methods by applying average precipitation data from 97 rain gauge stations in that province for a period of 20 years (1994–2014): Inverse Distance Weighting, Radial Basis Functions (Completely Regularized Spline, Spline with Tension, Multiquadric, Inverse Multiquadric, Thin Plate Spline), Kriging (Simple, Ordinary, Universal), Co-Kriging (Simple, Ordinary, Universal) with an auxiliary elevation parameter, and non-linear Regression. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R2) were used to determine the best-performing method of precipitation interpolation. Our study shows that Ordinary Co-Kriging with an auxiliary elevation parameter was the best method for determining the distribution of annual precipitation for this region, showing the highest coefficient of determination of 0.46% between estimated and observed values. Therefore, the application of this method of precipitation mapping would form a mandatory base for regional planning and policy making in the arid to semi-arid Khorasan Razavi province during the future.

Crack Control Technology of SPMT Transportation Structure of Long-span and Special-shaped Concrete Box Girder

By analyzing the engineering characteristics of SPMT transportation of long-span and special-shaped box girder, this paper took asynchronous displacement as the master control parameter of large concrete box girder transportation and stress as the auxiliary control parameter, and put forward the crack control method of spatial four-pivots driven concrete box girder transportation structure. Through numerical simulation, this paper set up the control values of girder posture and stress in box girder transportation, constructed the information monitoring system of girder posture and stress to realize remote real-time monitoring and real-time display, and shaped the stress and posture control technology of SPMT transportation structure for long-span specialshaped box girder, which helped the box girder of Cross Bay Link, Tseung Kwan O project to be successfully barged. The research results of this paper can be used for reference for similar projects in the future.

Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis

In this research, we study a weakly singular Volterra integro differential equation with Caputo‐type fractional derivative. First, we derive a sufficient condition for the existence and uniqueness of the solution of this problem based on the maximum norm. It is observed that the condition depends on the domain of definition of the problem. Thereafter, we show that this condition will be independent of the domain of definition based on an equivalent weighted maximum norm. In addition, we have also provided a procedure to extend the existence and uniqueness of the solution in its domain of definition by partitioning it. We also derive a sufficient condition under which the model problem will provide an analytic solution. Next, we introduce an operator‐based parameterized method to generate an approximate solution of this problem. Convergence analysis of this approach is established here. Next, we have optimized this solution based on least square method. For this, residual minimization is used to obtain the optimal values of the auxiliary parameter. In addition, we have also provided an error bound based on this technique. Several numerical examples are produced to clarify the effective behavior of the convergence of the present method. Comparison of the standard method and optimized method based on residual minimization signify the better accuracy of modified one. In addition, we also consider an equivalent form of weakly singular integro differential equation of Heat transfer problem to show the high effectiveness of the present approach.

Analysis of influences of pressure anisotropies on the 3D MHD equilibrium in LHD

3D equilibria with an anisotropic pressure component in the large helical device are analyzed with respect to their magnetic axis locations. The anisotropic extension of the 3D equilibrium solver variational moments equilibrium code, anisotropic neumann inverse moments equilibrium code, is used to compute fixed-boundary plasma equilibria based on a bi-Maxwellian distribution function describing the anisotropic particles. Different heating scenarios are assessed by means of parallel and perpendicular pressure anisotropies with different radial anisotropic pressure profiles imposed. A theoretical predicted scaling of the magnetic axis location with the auxiliary parameter βeq as predicted for classical stellarators and heliotrons by Hitchon [Nucl. Fusion 23, 383 (1983)] is found to be applicable to the large helical device in the case of a flat hot-particle profile for parallel or weak perpendicular dominated anisotropies with β⊥/β∥≤2. For strong perpendicular or non-flat hot-particle profiles, a deviation from the predicted scaling of the magnetic axis location is found. Whereas center-peaked profiles show a stronger shift of the magnetic axis, edge-peaked profiles show no significant change of its radial location. High critical magnetic fields are identified as a necessary condition for strong perpendicular anisotropies. The observed deviations are ascribed to the magnetic field structure and negative pressure gradients. The invalidity of the theoretical predictions in the case of certain configurations is found to be caused by higher-order terms in the pressure components, which are not accounted for by the ordering on which the theory is based.

A new fractional SICA model and numerical method for the transmission of HIV/AIDS

In this research, a new SICA model is proposed in a fractional framework for the HIV/AIDS transmission dynamics. The new model involves a Caputo‐type fractional derivative with a Mittag‐Leffler function as its nonsingular kernel. In addition, the resultant fractional equations avoid dimensional mismatching by using an auxiliary parameter. Furthermore, the nonnegativity of the solution, the equilibrium points, and their stability are studied. Additionally, we implement the model by a powerful approximation scheme based on the product‐integration rule. Comparative results with the real experimental observations, happened in Cape Verde Islands from 1987 to 2014, verify that the new fractional model is more efficient than the pre‐existent classical model with ordinary time derivatives. More to the point, the fractional order itself provides a degree of flexibility affecting the performance of the model, which is helpful to exhibit the hidden features of the disease transmission in an accurate, appropriate manner.

Pseudo-parameter Iteration Method (PIM): A semi-analytic solution procedure for nonlinear problems

We present an iterative semi-analytical method for solving not only nonlinear ordinary differential equations but partial differential equations. In this method, a system of nonlinear integral equations, equivalent to an original differential equation together with (initial and) boundary conditions, is constructed based on an artificially introduced (non-zero) parameter. The method finds a solution for the differential equation with the conditions by solving the integral equation system via the Banach contraction principle. The parameter, referred to as the pseudo-parameter, is a non-zero auxiliary (non-physical) parameter that provides a key to arrive at the integral equations from the differential equation. Further, the parameter can be viewed as a control parameter, which can control the performance of the method, e.g., its accuracy and convergence speed, etc. Especially, the present method, different from other nonlinear semi-analytic techniques such as the perturbation approach, does not depend on a small (perturbation) parameter, so that it can find a wide application in (strongly) nonlinear physical problems without a proper linearization strategy under small perturbations.

A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator

This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.

Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator

The current study is of interest when performing a useful extension of a crucial physical problem through a non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance (RC), Inductance-Capacitance (LC), and Resistance-Inductance-Capacitance (RLC) electric circuits utilizing a generalized type fractional operator in the sense of Caputo, called non-local M-derivative. Additionally, to keep the dimensionality of the physical parameter in the proposed model, we use an auxiliary parameter. Owing to the fact that all solutions depend on three parameters unlike the other solutions containing one or two parameters in the literature, the solutions obtained in this study have more general results. On the other hand, in order to observe the advantages of the non-local M-derivative, a comprehensive comparison is carried out in the light of experimental data. We make this comparison for the RC circuit between the non-local M-derivative and Caputo derivative. It is clearly shown on graphs that the fractional M-derivative behaves closer to the experimental data thanks to the added parameters α, ρ, and γ.

A Pulse-Number-Adjustable MSPCNN and Its Image Enhancement Application

Pulse-coupled neural network (PCNN) aims to control neuronal firing state automatically and complete related image processing tasks. This paper presents a pulse-number-adjustable MSPCNN model (PNA-MSPCNN) that can automatically acquire the firing times and the firing frequency of each neuron. Hereinto, synaptic weight matrix Wijkl and decay factor α will generate an interaction value to determine the final calculation result of the internal activity U. Dynamic threshold amplitude V, step function Q, and auxiliary parameter P can precisely adjust the variation ranges of the dynamic threshold E. Additionally, we propose a low-light image enhancement method based on the above PNA-MSPCNN and a modified low-light image enhancement (LIME). The proposed LIME algorithm focuses mainly on the parameter setting method of weight matrix Wmq, which will bring further improvement of testing image contrast. Experimental results demonstrate that our proposed method achieves better low-light image enhancement performances, compared to prevalent image enhancement methods, including SSIM of 0.8725, AMBE of 0.0550, MSE of 0.0092, and PSNR of 45.7764.